| 授業の目的 【日本語】 | | | The purpose of this course is to give an introduction to the theory of linear representations of groups, including finite groups and compact Lie groups. The focus will be on finite dimensional real and complex representations, although some general phenomena will be treated in a more general setting. The course will be taught in English with lecture notes provided at the beginning of each lecture. |
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| 授業の目的 【英語】 | | |
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| 到達目標 【日本語】 | | | The goal is to give participants a basic knowledge of representation theory, in general, and the finite dimensional representations of the classical (compact Lie) groups, in particular. |
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| 到達目標 【英語】 | | |
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| 授業の内容や構成 | | | The course will give an introduction to the theory of linear representations of groups, including finite groups and compact Lie groups. The focus will be on finite dimensional real and complex representations, although some general phenomena will be treated in a more general setting. |
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| 履修条件 | | | A working knowledge of basic undergraduate mathematics including calculus and linear algebra is required. |
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| 関連する科目 | | |
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| 成績評価の方法と基準 | | | Grading will be based on homework problems assigned every week. |
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| 教科書・テキスト | | | Vinberg, Ernest B. "Linear representations of groups." Translated from the 1985 Russian original by A. Iacob. Reprint of the 1989 translation. Modern Birkh?user Classics. Birkh?user/Springer, New York, 2010. vii+146 pp. ISBN: 978-3-0348-0062-4. |
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| 参考書 | | | Etingof, Pavel; Golberg, Oleg; Hensel, Sebastian; Liu, Tiankai; Schwendner, Alex; Vaintrob, Dmitry; Yudovina, Elena "Introduction to representation theory." With historical interludes by Slava Gerovitch. Student Mathematical Library, 59. American Mathematical Society, Providence, RI, 2011. viii+228 pp. ISBN: 978-0-8218-5351-1 Available at http://www-math.mit.edu/~etingof/repb.pdf. |
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| 課外学習等（授業時間外学習の指示） | | |
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| 注意事項 | | |
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| 他学科聴講の可否 | | |
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| 他学科聴講の条件 | | | Students, who do not major in mathematics, are asked to contact the instructor before the first lecture to discuss necessary background knowledge. |
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| レベル | | |
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| キーワード | | | Groups, Lie groups, linear representations. |
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| 履修の際のアドバイス | | | Participants are encouraged to ask questions during lectures. |
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| 授業開講形態等 | | |
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| 遠隔授業（オンデマンド型）で行う場合の追加措置 | | |
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